An iterative boundary element method for a wing-in-ground effect

International Journal of Naval Architecture and Ocean Engineering.
2014.
Jun,
6(2):
282-296

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

- Published : June 30, 2014

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NOMENCLATURE

INTRODUCTION

Effect of the ground has several impacts on a structure flying above the surface. These structures use the several benefits that the surface serves to them, which is named as ground effect flight. Different definitions of ground effect can be found in the literature and one of them defines it as “a phenomenon of aerodynamic, aeroelastic and aeroacoustic impacts on platforms flying in close proximity to an underlying surface” (
Reeves, 1993
; Rozhdestvensky, 2006). Efficient utilization of the ground effect proposed a different transportation technique other than mainly used, when the Russians first made use of it during the cold war (
Rozhdestvensky, 2006
).
Although first built for militaristic purposes, ground effect is a phenomenon that is generally exploited by Wing-in-Ground (WIG) effect crafts to improve transportation efficiency. Analyzing the Von Karman-Gabrielli Diagram (see
Fig. 1)
, WIG vehicles fill the gap between very efficient but slow conventional ships and not that efficient but very fast airplanes.
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FORMULATION OF THE PROBLEM

Incompressible and inviscid continuity equation for an irrotational fluid is defined by the Laplace Equation which states that the total potential
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NUMERICAL IMPLEMENTATION

It is possible to divide an arbitrary surface S into N panels to construct a numerical solution following Green’s identity with Dirichlet type of boundary condition given in Eq. (6). If Eq. (6) is to be performed for each panel of the surface (and the wake), we may write:
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- Direct boundary element method

The geometries inside the flow will be divided into panels and in each panel, there will be collocation points at which all the calculations will be made. On each collocation point, constant strength sources and constant strength doublets will be distributed and at all these collocation points Eq. (14) must be satisfied. Let’s say a body inside the fluid has
- Iterative boundary element method

When objects in the flow have complex shapes and must be represented by large amounts of panels, the sufficiency of a computer may be questioned. For example, if
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VALIDATION

- Validation with the single case

A wing in ground effect loses its advantage as it moves away from the ground. At infinite clearance, the wing will act like as if it is inside an unbounded fluid. If the ground is adequately far enough from the hydrofoil, then we must expect the hydrofoil to have its naked lift (as if there was nothing affecting the flow of the hydrofoil). To validate the results, a wing section of NACA6409 was chosen with the ground clearance selected to be
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Lift coefficients obtained for WIG effect and the single case.

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- Validation with direct BEM and CFD

As a first step, results derived with the boundary element and the Finite Volume Methods (FVM) were compared for a single NACA6409 with an angle of attack of 4° in an unbounded fluid. Due to the absence of the ground effect, direct BEM was used. Obtained lift coefficient values were in good agreement as BEM found 1.1982 while FVM found 1.1857 for the wing.
Fig. 7
shows the negative pressure coefficient distribution derived with BEM and CFD. Except the leading edge region of the suction side, both methods gave compatible results with each other.
To prove the effectiveness of the IBEM, the obtained results are compared with the results obtained with Direct BEM and CFD. This time, the same wing section was solved with ground clearance
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- Validation with results from the literature

Up to now, results found with IBEM seems to be in good agreement with the other methods. At this part of the paper, the results produced with the iterative method will be compared with the results found in the literature. This will be done in two steps. First, the lift coefficients produced with IBEM will be compared with
Abramowski’s (2007)
work and then the pressure distribution will be compared with the results produced by
Firooz and Gadami (2006)
.
Abramowski (2007)
have investigated the ground effect over a NACA/Munk M15 airfoil. Lift coefficients at different ground clearances have been found. Results found with IBEM is compared with the results in that study and this is given in
Fig. 9
.
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TIME CONSUMPTIONS

Applicability of the iterative method relies on the results of time consumption. Iterative boundary element method will be preferred in problems containing high number of panels which will give solutions slower. IBEM stores fewer values in the computer’s memory while the direct boundary element uses more computer memory. This difference between the stored values of both methods leads to differences in the acquisition of a solution. IBEM responds more quickly and gives faster results (
Kinaci et al., 2011
).
To fully comprehend the advantage IBEM offers, a test case of a two dimensional NACA6409 wing with 0° AoA in ground effect was solved in different clearances from the ground for various numbers of panels. The results of the test case are given in
Table 2
.
Distances in
Table 2
are dimensionless and given in
Time elapsed in seconds for direct (a) and iterative methods (b). Number of panels is listed vertically while distances are listed horizontally in these tables.

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GRID DEPENDENCY

Grid dependency is investigated by single precision BEM for a single NACA6409 wing at 4° of AoA. The lift coefficient and the pressure coefficient distribution along the wing is examined for 10, 20, 50, 100 and 250 panels. The lift coefficient vs. number of panels is given in
Fig. 12
.
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GROUND EFFECT ON A NACA6409 WING

Up to this point, the accuracy and the efficiency of IBEM was proved. The code developed with the theory of IBEM was then used to assess a two dimensional NACA6409 wing-in-ground effect. Extreme ground effect (which is when the wing is
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CONCLUSION AND FUTURE WORK

In this paper, an iterative boundary element method for a solution of the flow around a wing-in-ground effect was proposed. Compared to RANSE solutions BEM is quite faster; which only discretizes the body inside the fluid rather than the whole fluid domain. However, as shown in this paper, there are methods to increase the efficiency of BEM. Iterative BEM is faster and has good precision, therefore; it seems to be more efficient than direct BEM. Iterative method shows good prospect in dealing with geometries in ground proximity where a higher number of panels must be used. These may include complex bodies of three dimensions in which case the panels will no longer be represented by lines but surfaces which will increase the calculation time significantly. Quick assessment of the efficiency of a particular type of wing section for WIG crafts can be made with IBEM.
When the wing is in extreme ground effect, the wing will possibly oscillate in the air due to vortex separations from the body. This will create unsteady motions for the wing. Unsteady motions will lead the WIG problem to be solved at each time step increasing the necessity for quicker solutions. It is thought that IBEM will prove its real worth in unsteady cases where the solution time is expected to drop significantly. As a future work, the generated code will be developed for solving unsteady motions to include extreme ground effect cases.
Acknowledgements

This research has been supported by Yildiz Technical University Scientific Research Projects Coordination Department. Project No: 2013-10-01-KAP02. The author feels gratitude towards Prof. Sakir BAL due to his generous aids while developing the code and Prof. Mesut GUNER for supporting the work.

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Citing 'An iterative boundary element method for a wing-in-ground effect
'

@article{ E1JSE6_2014_v6n2_282}
,title={An iterative boundary element method for a wing-in-ground effect}
,volume={2}
, url={http://dx.doi.org/10.2478/IJNAOE-2013-0179}, DOI={10.2478/IJNAOE-2013-0179}
, number= {2}
, journal={International Journal of Naval Architecture and Ocean Engineering}
, publisher={The Society of Naval Architects of Korea}
, author={Kinaci, Omer Kemal}
, year={2014}
, month={Jun}